Multiphase modelling of vascular tumour growth in two spatial dimensions

In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model. Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters are investigated

A multiphase model describing vascular tumour growth

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found `in vivo' in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs

Exploiting the synergy between carboplatin and ABT-737 in the treatment of ovarian carcinomas

Platinum drug-resistance in ovarian cancers is a major factor contributing to chemotherapeutic resistance of recurrent disease. Members of the Bcl-2 family such as the anti-apoptotic protein Bcl-XL have been shown to play a role in this resistance. Consequently, concurrent inhibition of Bcl-XL in combination with standard chemotherapy may improve treatment outcomes for ovarian cancer patients. Here, we develop a mathematical model to investigate the potential of combination therapy with ABT-737, a small molecule inhibitor of Bcl-XL, and carboplatin, a platinum-based drug, on a simulated tumor xenograft. The model is calibrated against in vivo\ud experimental data, wherein tumor xenografts were established in mice and treated with ABT-737 and carboplatin on a fixed periodic schedule, alone or in combination, and tumor sizes recorded regularly. We show that the validated model can be used to predict the minimum drug load that will achieve a predetermined level of tumor growth inhibition, thereby maximizing the synergy between the two drugs. Our simulations suggest that the time of infusion of each carboplatin dose is a critical parameter, with an 8-hour infusion of carboplatin administered each week combined with a daily bolus dose of ABT-737 predicted to minimize residual disease. We also investigate the potential of ABT-737 co-therapy with carboplatin to prevent or delay the onset of carboplatin-resistance under two scenarios. When resistance is acquired as a result of aberrant DNA-damage repair in cells treated with carboplatin, the model is used to identify drug delivery schedules that induce tumor remission with even low doses of combination therapy. When resistance is intrinsic, due to a pre-existing cohort of resistant cells, tumor remission is no longer feasible, but our model can be used to identify dosing strategies that extend disease-free survival periods. These results underscore the potential of our model to accelerate the development of novel therapeutics such as ABT-737, by predicting optimal treatment strategies when these drugs are given in combination with currently approved cancer medications

Mathematical analysis of a model for the growth of the bovine corpus luteum

The corpus luteum (CL) is an ovarian tissue that grows in the wound space created by follicular rupture. It produces the progesterone needed in the uterus to maintain pregnancy. Rapid growth of the CL and progesterone transport to the uterus require angiogenesis, the creation of new blood vessels from pre-existing ones, a process which is regulated by proteins that include fibroblast growth factor 2 (FGF2).\ud \ud In this paper we develop a system of time-dependent ordinary differential equations to model CL growth. The dependent variables represent FGF2, endothelial cells (ECs), luteal cells, and stromal cells (like pericytes), by assuming that the CL volume is a continuum of the three cell types. We assume that if the CL volume exceeds that of the ovulated follicle, then growth is inhibited. This threshold volume partitions the system dynamics into two regimes, so that the model may be classified as a Filippov (piecewise smooth) system.\ud \ud We show that normal CL growth requires an appropriate balance between the growth rates of luteal and stromal cells. We investigate how angiogenesis influences CL growth by considering how the system dynamics depend on the dimensionless EC proliferation rate, p5. We find that weak (low p5) or strong (high p5) angiogenesis leads to ‘pathological’ CL growth, since the loss of CL constituents compromises progesterone production or delivery. However, for intermediate values of p5, normal CL growth is predicted. The implications of these results for cow fertility are also discussed. For example, inadequate angiogenesis has been linked to infertility in dairy cows

Solution to the problem of the poor cyclic fatigue resistance of bulk metallic glasses

The recent development of metallic glass-matrix composites represents a particular milestone in engineering materials for structural applications owing to their remarkable combination of strength and toughness. However, metallic glasses are highly susceptible to cyclic fatigue damage, and previous attempts to solve this problem have been largely disappointing. Here, we propose and demonstrate a microstructural design strategy to overcome this limitation by matching the microstructural length scales (of the second phase) to mechanical crack-length scales. Specifically, semisolid processing is used to optimize the volume fraction, morphology, and size of second-phase dendrites to confine any initial deformation (shear banding) to the glassy regions separating dendrite arms having length scales of ≈2 μm, i.e., to less than the critical crack size for failure. Confinement of the damage to such interdendritic regions results in enhancement of fatigue lifetimes and increases the fatigue limit by an order of magnitude, making these “designed” composites as resistant to fatigue damage as high-strength steels and aluminum alloys. These design strategies can be universally applied to any other metallic glass systems

Prevalence of sulfonamide resistance genes in bacterial isolates from manured agricultural soils and pig slurry in the United Kingdom

Prevalence of three sulfonamide resistance genes, sul1, sul2 and sul3 and sulfachloropyridazine (SCP) resistance was determined in bacteria isolated from UK manured agricultural clay soils and slurry samples, over a two year period. Slurry from tylosin-fed pigs amended with SCP and oxytetracycline (OTC) was used for manuring. Sul gene positive isolates were further screened for the presence of class 1 and 2 integrons. Phenotypic resistance to SCP was significantly higher in pig slurry and post application soil than in pre-application soil. Of 5isolates, 23 % carried sul1, 18 % sul2 and 9 % sul3 only. Two percent of isolates contained all three sul genes. Class 1 and class 2 integrons were identified in 5 % and 11.7 % of sul positive isolates. In previous reports, sul1 was linked to class 1 integrons, but in this study only 8 % of sul1 positive isolates carried the intI1 gene. Sulfonamide resistant pathogens were identified in slurry amended soil and soil leachate, including Shigella flexneri, Aerococcus spp. and Acinetobacter baumanni, suggesting a potential environmental reservoir. Sulfonamide resistance in Psychrobacter, Enterococcus and Bacillus spp. is reported for the first time, and this study also provides the first description of the genotype sul1, sul2 and sul3 outside the Enterobacteriacae, and in the soil environment

Inter-species variation in colour perception

Inter-species variation in colour perception poses a serious problem for the view that colours are mind-independent properties. Given that colour perception varies so drastically across species, which species perceives colours as they really are? In this paper, I argue that all do. Specifically, I argue that members of different species perceive properties that are determinates of different, mutually compatible, determinables. This is an instance of a general selectionist strategy for dealing with cases of perceptual variation. According to selectionist views, objects simultaneously instantiate a plurality of colours, all of them genuinely mind-independent, and subjects select from amongst this plurality which colours they perceive. I contrast selectionist views with relationalist views that deny the mind-independence of colour, and consider some general objections to this strategy